Related papers: Mixing and observation for Markov operator cocycle…

We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions in order to have some form of almost sure asymptotic synchronization,…

The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…

In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of…

In this paper we show how questions about operator algebras constructed from stochastic matrices motivate new results in the study of harmonic functions on Markov chains. More precisely, we characterize coincidence of conditional…

We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…

Using a Markov chain approach we rederive the exact density functional for hard rod mixtures on a one-dimensional lattice, which forms the basis of the lattice fundamental measure theory. The transition probability in the Markov chain…

We develop operator renewal theory for flows and apply this to obtain results on mixing and rates of mixing for a large class of finite and infinite measure semiflows. Examples of systems covered by our results include suspensions over…

This article extends the literature on copulas with discrete or continuous marginals to the case where some of the marginals are a mixture of discrete and continuous components. We do so by carefully defining the likelihood as the density…

When estimating finite mixture models, it is common to make assumptions on the mixture components, such as parametric assumptions. In this work, we make no distributional assumptions on the mixture components and instead assume that…

This paper draws distinctions among various concepts related to tipping points, robustness, path dependence, and other properties of system dynamics. For each concept a formal definition is provided that utilizes Markov model…

We consider an independently identically distributed random dynamical system generated by finitely many, non-uniformly expanding Markov interval maps with a finite number of branches. Assuming a topologically mixing condition and the…

The goal of this expository paper is to describe conditions which guarantee a central limit theorem for functionals of general state space Markov chains. This is done with a view towards Markov chain Monte Carlo settings and hence the focus…

We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these…

Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…

The paper deals with the problem of large-time behaviour of trajectories for discrete-time dynamical systems driven by a random noise. Assuming that the phase space is finite-dimensional and compact, and the noise is a Markov process with a…

We establish stability of random absolutely continuous invariant measures (acims) for cocycles of random Lasota-Yorke maps under a variety of perturbations. Our family of random maps need not be close to a fixed map; thus, our results can…

In this paper, we study dependence coefficients for copula-based Markov chains. We provide new tools to check the convergence rates of mixing coefficients of copula-based Markov chains. We study Markov chains generated by the…

We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. The technique generalizes the notion of…

Order-preserving couplings are elegant tools for obtaining robust estimates of the time-dependent and stationary distributions of Markov processes that are too complex to be analyzed exactly. The starting point of this paper is to study…

We provide the most general forms of covariant and normalized time operators and their probability densities, with applications to quantum clocks, the time of arrival, and Lyapunov quantum operators. Examples are discussed of the profusion…